I've lived in Washington my entire life, and I've never heard someone from here call then "brown bears".
The whole grizz in the Cascades thing is very confused.
Several biologists from the U.S. Fish and Wildlife Service and the Washington State Department of Fish and Wildlife believe that a few grizzly bears are present in the North Cascades. This is based on a few persistent sightings that possiblly are grizzly bears and the presence of quite a few grizzly bears in British Columbia. I agree it is unlikely that grizzly bears are particularly concerned with international boundaries.
I am far more skeptical. First off, on the Canadian side, there have been no reliable sightings of grizzly bears in either Manning Provincial Park or Cathedral Provincial Park in over twenty years. These two parks are just over the border from the Pasayten Wilderness. However, just north of Manning Park at a place called Paradise Valley you will almost certainly see a griz. There is no explaination for this distribution of bears. Logically, bears that are commuting southward would sometimes pass through Manning Park, and on the average you would expect they would be seen on their way through even if they were not resident.
Second, about five years ago there were surveys that attempted to use DNA analysis to find grizzly bears in the Washington Cascades. No grizzly DNA was found either in hair samples or scat.
Third, there have been several efforts using bait and motion-sensing cameras (these are cool gadgets). Lots of bears were observed, and a few were checked out more closely as possible griz, none of them could be confirmed. However, lynx and wolverine were identified here (which is very cool).
Fourth, there is a black bear hunting season here. It seems surprising to me that no bear hunter has mistakenly shot a grizz here. Although given the complications that such a kill would produce, maybe the people who shoot a grizz here are just laying low...
I'm real leery of a lot of visual observations. Large male black bears can appear to have a prominent hump. And most people don't end up with a lot of time to carefully observe the bears they see in the wild. We also prime people with the signs at trailheads, so hikers are kind of psychologically primed to interpret any bear sighting as a possible grizz.
My own bet is that it is far more likely that there is a resident grizz population east of the Cascades. This is largely because the area is considerably more isolated and because there are better corridors for bears to travel to the north.
This has been going on for almost two decades in the Cascades. The hard data keeps coming up zero. The sightings still trickle in, but any grizzly bears in the Cascades are remarkably elusive. The way I think about it, being mauled by a grizzly bear in Washington would probably get you on the cover of Outside magazine. And you'd confirm that there are grizzly bears here. That would be some consolation, I guess.